1. ## Functions

Question:
Find $\frac{f(x+h)-f(x)}{h}$ where h is not equal to zero and $f(x)=\sqrt{x}$.

Attempt:
$= \frac{\sqrt{x+h}-\sqrt{x}}{h}$
I have to rationalize the numrator
$= \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x}}$

Now how to simplify?

Thank you

2. Originally Posted by mj.alawami
Question:
Find $\frac{f(x+h)-f(x)}{h}$ where h is not equal to zero and $f(x)=\sqrt{x}$.

Attempt:
$= \frac{\sqrt{x+h}-\sqrt{x}}{h}$
I have to rationalize the numrator
$= \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x})}$

Now how to simplify?

Thank you
$\frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x})}=\frac{1}{(\sqrt{x+h}+\sqrt{x})}$